Question

Спростіть вираз:

1) (y + 3)/(2y + 2) - (y + 1)/(2y - 2) + 3/(y ^ 2 - 1) 2) (2b ^ 2 - b)/(b ^ 3 + 1) - (b - 1)/(b ^ 2 - b + 1)
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Answer 1

Ответ:

$\frac{y + 3}{2y + 2} - \frac{y + 1}{2y - 2} + \frac{3}{ {y}^{2} - 1} = \\ = \frac{y + 3}{2(y + 1)} - \frac{y + 1}{2(y - 1)} + \frac{3}{(y - 1)(y + 1)} = \\ = \frac{(y + 3)(y - 1) - (y + 1)(y + 1) + 6}{ (y - 1)(y + 1) } = \\ = \frac{ {y}^{2} + 3y + y - 3 - {y}^{2} - 2y - 1 + 6 }{ (y - 1)(y + 1)} = \\ = \frac{2y + 2}{ (y - 1)(y + 1)} = \\ = \frac{2(y + 1)}{(y - 1)(y + 1)} = \\ = \frac{2}{y - 1}$

$\frac{2 {b}^{2} - b }{ {b}^{3} + 1} - \frac{b - 1}{ {b}^{2} - b + 1 } = \\ = \frac{2 {b}^{2} - b }{(b + 1)( {b}^{2} - b + 1)} - \frac{b - 1}{ {b}^{2} - b + 1 } = \\ = \frac{2 {b}^{2} - b - {b}^{2} + 1 }{(b + 1)( {b}^{2} - b + 1)} = \\ = \frac{ {b}^{2} - b + 1 }{(b + 1)( {b}^{2} - b + 1)} = \\ = \frac{1}{b + 1}$